Advances in communications and digital multimedia technologies have fueled the demand for faster and more efficient wireless transmission of voice, data, and video on a global basis. Wireless transmission of information is accomplished by sending an information signal from a source to a destination via a wireless channel, which is a band of frequencies in the electromagnetic spectrum capable of serving as a transmission medium and carrying an information signal. Typically, the usable range of the electromagnetic spectrum allocated for wireless channels on any communication system is limited. For wireless phone systems, for example, the total bandwidth allocated is typically on the order of 50 MHz. As a result, multicarrier communication techniques and multiple access communication techniques capable of sharing and allocating the spectrum efficiently among many channels (multicarrier techniques) and many users (multiple access techniques) are required.
Multicarrier techniques are used in wireless communication systems to improve the bandwidth efficiency and reduce the intersymbol interference of the system. These techniques divide the usable spectrum among many channels and transmit data with multiple carriers. Multiple access techniques are used to increase the number of users that may access the wireless services provided by the system at any given time. Multicarrier and multiple access techniques can also be combined to serve many users simultaneously and provide them with the bandwidth efficiency and wireless services they so desire.
An example of a multicarrier technique include Orthogonal Frequency Division Multiplexing (“OFDM”). Examples of multiple access techniques include Frequency Division Multiple Access (“FDMA”), Time Division Multiple Access (“TDMA”), and Code Division Multiple Access (“CDMA”) and its many variations. Examples of combined multicarrier/multiple access techniques include Orthogonal Frequency Division Multiple Access (“OFDMA”), Multicarrier Code Division Multiple Access (“MC-CDMA”), and Multicarrier Direct Sequence CDMA (“Multicarrier DS-CDMA”),
Among the multicarrier and multiple access techniques available today, OFDM and OFDMA have emerged as attractive and powerful choices due to their robustness against multipath fading and high spectral efficiency. OFDM is currently used in the European digital audio and video broadcasting standards, and in digital terrestrial TV broadcasting. OFDM-based hybrid multiple access systems such as MC-CDMA are being considered for third-generation wireless communications systems. The wireline digital subscriber line (“DSL”) is based on OFDM. OFDM also outperforms FDMA and TDMA under many channel conditions, and is capable of outperforming CDMA in both single and multi-cellular-based systems.
OFDM achieves high spectral efficiency by dividing the available spectrum into multiple narrowband channels having carriers that are overlapping and orthogonal. Each carrier is at a different frequency and modulated by a given data symbol representing the information to be transmitted. The particular way in which the information is represented depends on the modulation scheme used, which may include phase shift keying (“PSK”) and its common variations such as differential phase shift keying (“DPSK”) and quadrature phase shift keying (“QPSK”), and quadrature amplitude modulation (“QAM”), among others.
A schematic diagram of a wireless communication system employing OFDM is shown in FIG. 1. The transmitted information signal consists of a linear combination of translations in the time-frequency space of a prototype pulse shape ψ defining the carriers, i.e.,
                              x          ⁡                      (            t            )                          =                              ∑                          k              ,              l                                ⁢                                    c                              k                ,                l                                      ⁢                          ψ              ⁡                              (                                  t                  -                  kT                                )                                      ⁢                          ⅇ                              2                ⁢                π                ⁢                                                                  ⁢                ⅈ                ⁢                                                                  ⁢                lFt                                                                        (        1        )            where Ck,l are the information-bearing data symbols, chosen from some finite alphabet constellation of a given modulation scheme, T is the symbol period and F is the separation between the multiple carriers. With W denoting the total bandwidth available for transmission, then N=W/F denotes the number of carriers used in the system.
The time-frequency translations of the prototype pulse shape ψ defining the carriers may be denoted by ψk,l as:ψk,l(t)=ψ(t−kT)e2πilFt  (2)A function family of pulse shapes identifying the OFDM system may therefore be represented by the triple (ψ,F,T).
A necessary condition for perfect reconstruction of the transmitted signal at the receiver is that the functions ψk,l are linearly independent (regardless of whether they are orthogonal or not), which implies that TF≧1. The OFDM system (ψ, F,T) is orthogonal if the following condition is satisfied:
                              〈                                    ψ                              k                ,                l                                      ,                          ψ                              m                ,                n                                              〉                =                  {                                                                      1                  ,                                                                                                  if                    ⁢                                                                                  ⁢                    k                                    =                                                            m                      ⁢                                                                                          ⁢                      and                      ⁢                                                                                          ⁢                      l                                        =                    n                                                                                                      0                                            else                                                                        (        3        )            where <ψ,φ> denotes the inner product between two functions ψ and φ.
The orthogonality of the functions ψk,l is not a requirement for perfect reconstruction at the receiver, but minimizes the error caused by additive white Gaussian noise (“AWGN”). The spectral efficiency ρ of the OFDM system in terms of data symbols transmitted per second per Hertz (“Hz”) is approximately given by ρ=1/(TF). Since TF≧1, the maximal spectral efficiency of an OFDM system is given by ρ=1.
Ideally, one would like to construct an OFDM system (ψ, F, T) that satisfies the following three conditions simultaneously: (1) the functions ψk,l should be orthogonal; (2) the pulse shape ψ should be well localized in time and frequency; and (3) TF=1, that is, the OFDM should have maximal spectral efficiency. The first condition, as mentioned above, is desired because of the error minimization in the presence of AWGN. The second condition, that of good time-frequency localization, is important because it leads to the use of a simple equalizer and reduces timing errors effects, frequency offset error effects as well as out-of-band interference, i.e., the leakage of signal energy outside the assigned transmission bandwidth. And the third condition is important as it enables the OFDM system to utilize the allocated spectrum efficiently.
As is well known in the art, the three conditions cannot be satisfied simultaneously due to the Balian-Low theorem. This is the case even if the orthogonality condition is relaxed in favor of biorthogonality, which would increase the sensitivity of the OFDM system to AWGN. As a result, OFDM systems available today employ a number of techniques to achieve the conditions above while attempting to optimize other factors in the system, such as intersymbol interference (“ISI”), interchannel interference (“ICI”) Doppler effect, delay spread and overall system performance in the presence of fading. ISI is caused by time dispersion due to multipath propagation, and ICI results from frequency distortion due to the Doppler effect.
Standard OFDM systems use rectangular pulse shapes and employ a guard interval or cyclic prefix to combat ISI. The main problem with OFDM systems using a guard interval or cyclic-prefix is that the pulse shapes are poorly localized in the frequency domain, which severely limits their performance characteristics in wireless channels and leads to complicated and expensive equalizer design. Additionally, the use of guard intervals or cyclic-prefix does not reduce ICI. This can result in additional loss of spectral efficiency since the carrier signals cannot be placed across the entire available spectrum. If filtering is applied to reduce ICI, the carrier signals are no longer orthogonal, which increases interference and reduces performance. OFDM systems that use a guard interval or cyclic prefix have TF>1 and thus achieve a spectral efficiency of less than 1, typically ρ=¾ or ⅘.
To address the drawbacks of using a guard interval or cyclic-prefix in an OFDM system, pulse-shaping OFDM systems have been proposed. The idea is to construct pulse shapes ψk,l that are well-localized in some sense in time and in frequency, in order to combat both ISI and ICI. For example, U.S. Pat. No. 5,790,516 describes pulse shaping methods that are based on a simple filtering of the transmission signal. The methods described therein, however, do not preserve the orthogonality of the pulses ψk,l and therefore result in interference between the pulses, leading to a loss of performance in the system.
Other pulse shaping methods described in the prior art, for example, those described in U.S. Pat. No. 6,278,686 and U.S. Pat. No. 6,584,068, are very restrictive, as they are only designed for Offset-QAM OFDM (“OQAM/OFDM”) and thus for a very limited choice of the parameters T and F. Although OQAM/OFDM maintains maximal spectral efficiency and allows for pulse shapes that are well localized in the time-frequency domain, it leads to increased complexity of the receiver. Furthermore, the pulse shaping methods described in these patents lead to pulses that are of infinite support in time and in frequency, which makes them of limited use in practice. In addition, those methods are not capable of constructing pulses that obey a prescribed spectral mask or a prescribed number of taps.
In view of the foregoing, there is a need in this art for a pulse shaping method for OFDM that combats both intersymbol and interchannel interference while maintaining high spectral efficiency.
There is a further need in this art for a pulse shaping method for OFDM that produces mutually orthogonal transmission pulses that have a prescribed number of taps and show fast spectral decay.
There is also a need in this art for a pulse shaping method for OFDM that is computationally efficient and produces orthogonal pulse shapes that are well localized in time and in frequency.